We consider economies with incomplete markets, one good per state, two periods,
=0, 1, private ownership of initial endowments, a single firm, and no assets other than shares in this firm. In Dierker, Dierker, Grodal (2002), we give an example of such an economy in which all market equilibria are constrained inefficient. In this paper, we weaken the concept of constrained efficiency by taking away the planner’s right to determine consumers’ investments. An allocation is called minimally constrained efficient if a planner, who can only determine the production plan and the distribution of consumption at
=0, cannot find a Pareto improvement. We present an example with arbitrarily small income effects in which no market equilibrium is minimally constrained efficient.